But playing at 1080p, you'll need more than 1GB if playing with all the settings maxed. But with a 560, you would probably playing at high anyways, not ultra.
I'm torn between building my first computer and just paying for one that I see advertised on ibuypower.com. It seems like they are very competitive in price with all the good components. This is what I'm looking at:
Case 1 x NZXT Tempest EVO Gaming Case-Black
Processor 1 x Intel® Core™ i5-2550K Processor (4x 3.40GHz/6MB L3 Cache)
Processor Cooling 1 x Liquid CPU Cooling System [SOCKET-1155]-[Free Upgrade] Standard 120mm Fan
Memory 1 x 8 GB [2 GB X4] DDR3-1600 Memory Module-Corsair
Video Card 1 x NVIDIA GeForce GTX 560 Ti - 1GB-Single Card
Motherboard 1 x Gigabyte GA-Z68AP-D
Motherboard USB / SATA Interface 1 x Motherboard default USB / SATA Interface
Power Supply 1 x 650 Watt - Casegears ECO-Element / 80+
Primary Hard Drive 1 x 120 GB ADATA S510 SSD-Single Drive
Data Hard Drive None
Optical Drive 1 x [12X Blu-Ray] LG BLU-RAY Reader, DVD±R/±RW Burner Combo Drive-Black
Flash Media Reader / Writer 1 x 12-In-1 Internal Flash Media Card Reader/Writer-Black
Sound Card 1 x 3D Premium Surround Sound Onboard
Network Card 1 x Onboard LAN Network (Gb or 10/100)
Operating System 1 x Microsoft Windows 7 Home Premium + Office Starter 2010 (Includes basic versions of Word and Excel)-64-Bit
that's not bad but building would be closer to 1000 if not 900, also, unless it's only like 5 mucks, the 2500k would be better, the difference is 1 on the multiplier which you can do with the stock cooler easily.
I'd say 2GB over the ti personally. Though like linkin said, 2GB ti would be preeety nice. If you don't plan on overclocking (I'm not sure why you wouldn't want to) then get the ti. If you plan in overclocking then I'd say the 2GB 560.
I would recycle my old HD for the added storage and use the SSD for gaming.
Upgrading from the Ti 1gb to the Ti2g is only about $39. Sounds like a no brainer from what everybody is saying.